Question

simplify.
\sqrt{8}

Explanation:

Step1: Factor the radicand

We know that \( 8 = 4\times2 \), so we can rewrite \( \sqrt{8} \) as \( \sqrt{4\times2} \).

Step2: Use the property of square roots

The property of square roots states that \( \sqrt{ab}=\sqrt{a}\times\sqrt{b} \) (where \( a\geq0 \) and \( b\geq0 \)). Applying this property to \( \sqrt{4\times2} \), we get \( \sqrt{4}\times\sqrt{2} \).

Step3: Simplify \( \sqrt{4} \)

Since \( \sqrt{4} = 2 \), we substitute this back into the expression, so \( \sqrt{4}\times\sqrt{2}=2\times\sqrt{2}=2\sqrt{2} \).

Answer:

\( 2\sqrt{2} \)